Trigonometeric function generation for use in digital signal processing

Abstract

A sequence of N sine and/or cosine values, e.g. for Fourier Transforms, quadrature demodulation or test tone generation, is produced by interpolation from a geometrically-spaced table of initial sine values using a first interpolation formula. After being output, each sine value is replaced in the table by a further calculated value, so the sine table size is kept at M = (Log2N)+2 (where N is the number of sine values in the sequence). To avoid round-off errors at widely-spaced interpolations, a second interpolation formula is selectively used in which sine values are interpolated from cosine values. A cosine table is therefore maintained concurrently with the sine table.

I claim: 
     
       1. A digital signal processing device comprising an input for receiving an input electrical signal, an output for making an output electrical signal available, and electrical processing circuits for processing the input signal to produce said output signal, the processing circuits including an electrical trigonometric function generator for generating a value of a trigonometric function in response to an input argument provided by said electrical processing circuits, said trigonometric function generator comprising: electrical input elements for receiving an input argument; first electrical storage elements for storing digital values of the function corresponding to spaced argument values; and arithmetic circuitry associated with said first electrical storage elements for interpolatively calculating, using a first algorithm, values of the function corresponding to arguments lying in the spaces between said spaced argument values; second electrical storage elements for storing digital values of a second, complementary function corresponding to spaced argument values;   said arithmetic circuitry also being associated with said second electrical storage elements for interpolatively calculating, using a second algorithm, values of said function corresponding to arguments lying in the spaces between said spaced argument values from values of the second complementary function corresponding to the neighbouring predetermined argument values; and   electrical logic control elements for selectively employing the second storage elements and algorithm for an input argument if use with said first store and said first algorithm gives rise to a substantial round-off error.   
     
     
       2. A digital signal processing device according to claim 1, wherein the function is a sine function and the complementary function is a cosine function, or vice versa, or a function derived therefrom. 
     
     
       3. A digital signal processing device according to claim 1 or claim 2, further comprising electrical elements for supplying an incremental (or decremental) sequence of arguments to said electrical input elements, whereby the function generator output comprises a time sequence corresponding to the function. 
     
     
       4. A digital signal processing device according to claim 3, wherein the first electrical storage elements are dimensioned to store fewer than the total number of function values which will be generated, and the arithmetic circuitry is arranged to calculate a further function value, and to replace an output function value in the first electrical storage elements with the further function value. 
     
     
       5. A digital signal processing device according to claims 1 or 2, in which the arithmetic circuitry is arranged to also generate, for the or each input value, the value of the complementary function. 
     
     
       6. A digital signal processing device according to claims 1 or 2, further comprising analogue output circuits for producing an analogue output corresponding to the generated digital function value. 
     
     
       7. A digital signal processing device according to claims 1 or 2, further comprising analogue output circuits for producing an analogue output corresponding to the generated digital function value, and wherein said digital signal processing device is used to generate tones. 
     
     
       8. A device according to claim 2, in which the electrical processing circuits are arranged to perform a spectral transform operation. 
     
     
       9. A device according to claim 8, wherein the transform operation is a Fourier transform.